https://file.aiquickdraw.com/mathbot/file/1729843187856y7yc8e73.jpg

Let's go through the questions from the image and provide solutions:

---

**1. Sederhanakanlah! (Simplify)**

a. \( 10^5 \times 10^5 : 10^9 \)

\[
= \frac{10^5 \times 10^5}{10^9}
= \frac{10^{10}}{10^9}
= 10^{10 - 9} = 10^1 = 10
\]

b. \( 1.234^4 : 1.234^4 \)

\[
= \frac{1.234^4}{1.234^4}
= 1
\]

c. \( (5^2)^5 : 5^{10} \)

\[
(5^2)^5 = 5^{2 \times 5} = 5^{10}
\]
\[
\frac{5^{10}}{5^{10}} = 1
\]

---

**2. Tentukan hasil dari! (Determine the result)**

a. \( \sqrt{40} \)

\[
\sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}
\]

b. \( \sqrt{18} + \sqrt{32} + \sqrt{9} \)

\[
\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}
\]
\[
\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}
\]
\[
\sqrt{9} = 3
\]
\[
3\sqrt{2} + 4\sqrt{2} + 3 = 7\sqrt{2} + 3
\]

c. \( \sqrt{36 + 64 - \sqrt{9 + 16}} \)

\[
\sqrt{36 + 64 - \sqrt{9 + 16}} = \sqrt{100 - \sqrt{25}} = \sqrt{100 - 5} = \sqrt{95}
\]

---

**3. Tentukan hasil dari logaritma dibawah! (Find the result of the logarithm below)**

a. \( \log_5 25 \)

\[
\log_5 25 = \log_5 5^2 = 2
\]

b. \( \log_2 8 \)

\[
\log_2 8 = \log_2 2^3 = 3
\]

c. \( \log_3 81 \)

\[
\log_3 81 = \log_3 3^4 = 4
\]

---

**4. Tentukan nilai \( x \) dari nilai mutlak dibawah! (Find the value of \( x \) from the absolute value below)**

a. \( |2x - 3| = 5 \)

\[
2x - 3 = 5 \quad \text{or} \quad 2x - 3 = -5
\]
\[
2x = 8 \quad \text{or} \quad 2x = -2
\]
\[
x = 4 \quad \text{or} \quad x = -1
\]

b. \( |7x + 9| = (-12) \)

This equation has no solution because the absolute value cannot equal a negative number.

---

Let me know if you would like further explanations or if you have any specific questions!

---

### 5 Relative Questions:
1. How do you simplify expressions involving powers of 10?
2. What is the procedure for simplifying square roots of non-perfect squares?
3. Can you explain how to solve logarithmic equations with different bases?
4. How can we approach solving absolute value equations with multiple possible solutions?
5. What are the properties of absolute values and why can't they be negative?

### Tip:  
For logarithms, remember that changing the base to match the number being logged can greatly simplify the calculation!

1. Sederhanakanlah! (Simplify): a. 10^5 x 10^5 : 10^9 b. 1.234^4 : 1.234^4 c. (5^2)^5 : 5^10 
2. Tentukan hasil dari! a. √40 b. √18 + √32 + √9 c. √36 + 64 - √9 + 16 
3. Tentukan hasil dari logaritma dibawah! a. ⁵Log 25 b. ²Log 8 c. ³Log 81 
4. Tentukan nilai x dari nilai mutlak dibawah! a. |2x - 3| = 5 b. |7x + 9| = (-12)

Simplify exponent expressions, evaluate square roots, solve logarithmic equations, and find solutions to absolute value equations. These problems are suitable for high school students in Grades 10-12, covering core algebraic concepts with step-by-step solutions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation